And I Couldn’t Even Get the Math Right

By JoCo October 18, 2010

I heard first through Twitter, but later through many of your emails and comments that Benoit Mandelbrot died on Thursday at 85. I can remember stumbling across his book “The Fractal Geometry of Nature” in my high school library, reading it and not really understanding it, but finding it mind blowing nonetheless. To me, that particular brand of hazy understanding feels like the correct way to think about a lot of things – fractals, electron clouds, cats in boxes waiting to be poisoned – the natural world is really too complicated and beautiful for any of us to fully understand, and that’s OK. That’s in fact what makes it so beautiful.

Many of you have asked if I’m planning on changing the lyrics or retiring the song. I’m not sure yet, but I don’t think I’ll do either of those things. I like the song and it would be a shame not to play it anymore, so retiring it is extremely unlikely. Changing the lyrics, I don’t know. On the one hand, the song is now factually inaccurate. Of course that hasn’t stopped me before. As many of you have pointed out, my description of the Mandelbrot Set in the song is at best incomplete, and at worst plain wrong. This failing of mine is even mentioned in the wikipedia article about the set, so that’s great (although if you look at the Popular Culture section of that article you’ll see that Arthur C. Clarke seems to have gotten it even more wrong than me – just saying).

On the other hand, that’s the song. It’s how I wrote it, and it was true then. It’s a snapshot of a certain time. I’ve never fixed the math error and it never bothered me all that much because you know, close enough. In the Times obit Mandelbrot is quoted as saying that he didn’t really like to prove his insights, he mostly liked to make crazy conjectures to make everyone think about stuff. That sounds about right to me. I like to think that Mandelbrot in particular would appreciate the “close enough” nature of my description. (And just to answer another FAQ, I know he’s heard the song: he talks about it briefly in this Big Think Interview.)

Not to get too heavy on you, but truth itself has a kind of fractal component – you can be right at one scale, but then zoom in and discover you had it all wrong. I stopped trusting people with absolute opinions the day I understood the answer to the question “How long is the coast of Britain?” is “It depends.” Not coincidentally that was the same day I discovered Mandelbrot. That was the question that led him to invent a new branch of mathematics by creating a way to quantify and discuss this kind of weirdness, and it changed the way we think about all sorts of things.

I’m leery of writing this post because I wouldn’t feel right about becoming the artist with the Official Mandelbrot Mourning Song. But it’s true that I still get a little misty when I sing those lyrics and remember what they mean to me – that everything around us is at least a little weird and unknowable and that’s the way it’s supposed to be.

That caveat aside, I leave you with one of my favorite fan videos, chalkboard animation made a few years ago by some Cornell students. I’m grateful to geekdad for reminding me that it existed.


Chase says

I couldn't disagree more with the sentiment expressed about how nice it is that we can never understand the beauty and complexity of nature. The amazing thing is that you CAN understand nature... it ain't necessarily easy but we've gotten a long, long way! And it gets more beautiful the more you understand, because underneath the ooh and ahh of the first glimpse there's so much more to ooh and ahh over, whether it's tiny proteins climbing along DNA to read the sequence and make more little tiny proteins that walk on other parts... to a whole universe where stars get born and explode and make other stars and eventually pump out the stuff to make those tiny little proteins millions of years later. It's not indecipherable -- it's all out there. Mandelbrot didn't sit around and smile about how fluffy and nice math is -- he worked it out! And other people could take what he did and learn even more... you can't just write that all off and say -- "Oh it's just too amazing for people to understand. That's why it's beautiful." Bullshit. That's bailing out of the game instead of playing.

As maybe you can't tell, I am a big fan.

(otherwise I wouldn't care what you said)

shadowfirebird says

I'm glad that you're not planning to change the lyrics; I had wondered.

You would have to lose a hell of a line if you did so. Makes me giggle every time I play the song.

Zarggg says

You don't need to change the lyrics. The song is still awesome.

But perhaps a small snippet paying homage to him referencing that line.

Chase says

Well, Feynman was a jerk. I do get your point, I think. But there's a real and interesting argument to be had about whether there is really a difference between "explaining/describing" and "understanding."

JonStrickland says

Clearly, what you need to do is write a song describing why you don't need to change the lyrics in this song. Or you'll have to buy another cool gadget akin to the ZenDrum you got for Mr. Fancy Pants to help balance out the need for the explanation.

Jess says

Re: the comments between Chase and JoCo, I think the song says it all - you can change the world in a tiny way. It seems incredibly unlikely that any one person will ever understand everything about how the universe functions (let alone the why of everything), but that people keep striving to understand pieces of it is noble. It also seems unlikely that even the human race as a whole will ever understand everything, as pretty much everything we uncover creates as many questions as it answers, but that we keep trying to understand more and more about our world is one of our best qualities, and Mandelbrot, like all great minds, is a part of that because he proved it worked, that all of our attempts to understand our world can actually go somewhere.

I can see the argument for changing the lyrics, and it does make a decent 'in' joke to say that Mandelbrot’s in heaven and no longer teaching math at Yale, but actually I think the song as it stands makes a very good eulogy. It highlights the fact that he was just a person doing something that interested him, that happened to discover something completely ground-breaking. Presumably he didn’t think it would make him rich and famous, he just thought it was cool. And then he went back to his day job as a professor.

W00t, presenting my opinions to the internet for no good reason!

SteveMalsam says

Yes! Add another verse to the song, played with the ZenDrum.

Sean Dague says

JoCo, I love the song, and I'm really hoping that it will be in your set list at w00tstock NYC.

John Darc says

In your defense, you did say he'd be in heaven when he was dead. Who's to say that isn't true?

Joel P says

Chase, I disagree. Fractals (and quantum mechanics) tell us to continue trying to get closer to truth even as we know it's an unreachable goal. We'll never get to the end of a fractal, and you can never get to a level of precision behind quantum uncertainty, and we'll never get any field of science 100% right either. Of course we've made enormous strides in science in recent history. We know 1000 times as much as we did 200 years ago. But it's meaningless to assert we're 1%, 50%, or 99.99999% through with the journey.

Science is always wrong. You don't change what's wrong, you build on it and try to be a little (or a lot) less wrong next time. They Might Be Giants put their longstanding classic "Why Does The Sun Shine?" on their most recent kids album (Here Comes Science), but they dealt with the fact that it's almost entirely scientifically inaccurate by following it with a new song "Why Does The Sun Really Shine?", containing lyrics like "Forget that song/They got it wrong/That thesis has been rendered invalid".

Don't change the song. If you want, change that lyric when you sing it live, but yes, this song was the truth when you wrote it. We only learn from our mistakes (and I use that term very very loosely here) if we have the courage to admit them and live with them.

Tansunn says

You don't need to rewrite the song, just end it after the line, "Mandelbrot's in heaven."

Gina says

On facebook a friend wondered if you would still play the song or change the lyrics. I replied that you would probably still play the song, and not change the lyrics, but that you would explain before performing it that when you wrote the song, Mandelbrot was Still Alive.


SSteve says

Changing the lyrics to be currently factually correct is a slippery slope that you don't want to start down. Why? Three words: Kenesaw Mountain Landis.

JoCo says

@Chase: sorry, one more. I am talking so much only because I think it's an interesting discussion (still a fan).ödel's_incompleteness_theorems

To paraphrase Godel: the game is rigged.

Also: there is no spoon.

Penguin says

I think the lyrics are fine as they are. The second verse covers both sides, life and death. So in a sense, the song is acknowledging his death already, because now when people listen they will take into account the line 'Mandelbrot's in heaven/at least he will be when he's dead' more than previously, because now he HAS passed on, if that makes sense? Heh, maybe just me. xD
I just loved playing with fractal generators when I was a kid and thinking about how strange the name 'Mandelbrot' sounded, made me think of vocoders for some reason. :D

Dan says

Though I understand what you are saying in your post, you must also understand that many people consider the declaration of him still being alive to be in very bad taste. I say this because I fit into this category. That being said, I'm not going to tell you what to do with your lyrics. I only ask to consider the bad taste angle.

Etienne says

Han shot first. Don't change it...

It's not in bad taste, it is an expresison of a moment in time.

Jonathan S. says

"To paraphrase Godel: the game is rigged.

Also: there is no spoon."

But will there at least be cake???

Chase says

Does Goedel really tell us that we can't understand everything? It's a pretty weighty thing for people who do formal math and such that it turns out to be impossible to have a completely airtight system where you can prove everything that you know is true is true. But that's just another step in understanding things better.

And don't sneak in "viscerally experience" in place of "understand." They're different and not mutually exclusive. I really love seeing a pretty rainbow or a sunset, just like I did before I ever heard of Rayleigh scattering. I think I even like them more for knowing a little bit about what's going on.

OK I need to go figure out when I became such an angry know-it-all. I think it happened at a Best Buy.

Chase says

I'm such a dork that I wrote "And now, to blow your mind, I will describe and explain things I do not understand." at the beginning of the last comment post, but not enough of a geek to realize the pointy brackets I used for dramatic effect would make it into HTML that wouldn't appear.

SquareWheel says

Heyyy, Feynman wasn't a jerk, he just lacked social skills. ={

Glad to hear your opinion on this, John. I still get a little misty about Mendelbrot's passing myself.

Azz says

For myself, I'm probably going to just take a moment of silence after "Mandelbrot's in heaven" when I'm singing along, and pick up again a little bit later.

Mike Ogilvie says

Woo-hoo! Point for JoCo for cogent use of the word "grok".

JonathanL says

Mandelbrot is one of my favorite songs of yours. I thouhgt it was col that there was a song about a weak subject for me that's also about this modern genius, and even if it isn't perfectly accurate, it's super-catchy and I'm sure most of your audience didn't even know who Benoit Mandelbrot was before the song; I know I didn't. I heard he passed and immediately thought of the song, and of course the lyrics about his "passing", and I hope you don't ever change them. Mandelbrot's contributions will teach forever, at Yale and the world over.

Understanding the very nature of our world is both terrifying and fascinating. I look forward to humanity's continued unravelling of this giant ball of yarn, even if that only seems to make the ball bigger with every new discovery.

Jerry says

Actually, from what I can tell from Mandelbrot's Wikipedia page, the biographical part of the song hasn't been 100% accurate since 2005 (when he apparently retired from teaching at Yale). So I wouldn't worry about changing it just for the sake of accuracy.

That said, I happen to agree with Azz that a moment of silence there in live performances, at least for the next few months or so, would be particularly poignant. It'd be simple enough (and fit remarkably well with the rest of the song).

"Mandelbrot's in heaven . . . He gave us order out of chaos..."

It would require a slight change in the tone of the song (since you'd be committing to the more sober, reflective tone of the verse that was previously teased when it was merely a lead-in to the joke about actually being alive), and I don't think that you'd want to make it a permanent change to the song, but it'd be a nice tribute to use in the immediate future.

BR says

I'm a math geek, and Mandelbrot was my first JoCo song which was linked to me way back during thing-a-week. Very sad news for me.

Mike says

A person writes a song and then puts it out into the world, and, in a way, it grows and belongs to everyone. It becomes part of their lives and their memories to the point that they can't even think of certain scenes or times in their lives without thinking of the song too. I'm against revisionism when it comes to songs and movies. Whenever I've heard a song with the lyrics changed or seen a movie that has been altered (Solo shot first!) it feels like the person doing the changing was reaching into MY past and changing something that was in MY head and I was powerless to fight back. It is closest I ever want to be to being strapped down to an operating table against your will and having your memories altered.

Krystal says

JoCo said, "There’s a difference between explaining/describing something and “understanding” it."

As an evolutionary biologist, the goals of my research are specifically to DESCRIBE patterns of diversity, and EXPLAIN the processes that produce them. I can't UNDERSTAND the myriad of stochastic events that contribute to changes in allele frequencies over time (=evolution), nor can anyone else (in my opinion), but the lack of absolutes is what keeps us all playing the game.

Ethan says

I've been listening to this song all day; I started listening to it when I heard that Mandelbrot had died, and well, I kept listening to it because I still love it. Thanks, JoCo, for making it in the first place, and I can totally get behind your reasons for not changing it.

LarryS says

RIP...may your trip to what waits beyond be not near as messy as the set of complex numbers you left us with in this life. RIP Sir

Karla says

Yay, I was hoping you would make a post about this. I definitely don't think you should change the lyrics. I think you're completely right about this song being a snapshot of a particular time and place and with it you can keep the memory of him alive for years and years to come.

Jen says

Medieval magicians wanted to know nature as a lover, to grok her infinitely even if it meant losing themselves.

Enlightenment-era scientists wanted to own nature, to plow her, to use her as God intended nature for man's use just as he intended woman for man's use.

Who's enlightened here, again?

Take a look at Evelyn Fox Keller, "Spirit and Reason at the Birth of Modern Science."

Anonymous Al says

Sorry, totally off topic here. Maybe a dumb question, but is there a date (or an approximate ballpark date) that the new studio album is going to be completed?

And, on topic, my fiancée proclaimed this to be the worst song EVAR when she first heard it (by playing it on Rock Band). After hearing it live, she cannot stop singing this song (almost to the point where I beg her to sing something else...ANYTHING else).

Gregor says

Chase wrote: "Bullshit. That’s bailing out of the game instead of playing."

Don't you see that "not understanding" is what drives the game in the first place. What's the fun in researching answered questions?

I can totally see what you're saying, and I can point to many times when people choose ignorance because it's too hard, too 'irrelevant' or inconvenient to their world views. These people bail out of the game.

Jonathan, however, isn't advocating bailing out, but simple pointing out that if we were able to fully understand our world, there would be no game to play.

That actually happened in physics for about a century, by the way. People largely stopped playing the game not because they were closed-minded, but because they thought Newton had answered the question. Thank goodness Einstein, et al, pointed out the holes in our understanding and re-opened the playing field.

We aren't likely to ever fully "understand" the universe, not because it is not knowable, but because we will continue to grow in our ability to observe and measure phenomena, and in our sophistication in describing what we see. Knowing that we don't fully understand is what keeps us playing.

Mike Selinker says

In case folks are interested in hearing more, Jonathan and I talk about the subject on Decode site.

I particularly like the comment from the reader who says that the Specials didn't change the words to "Free Nelson Mandela" either.


Mike Selinker says

Let me try that link again: this site here.


Sean Bowman says

Heh, I had a hunch you would write something about this. It's kinda cool to see that people asked you the same questions I was wondering about myself.

I won't go into details about it but a personal philosophy of mine is that you shouldn't change the art you create because it fragments the experience for others. Could even jeopardize the memory of the point in time when you wrote it.

However, a neat idea would be performing the song with alternate lyrics to be factually correct. A concert after all, is a new memory of that moment in time, taking into consideration what has happened since it was written. It would even be a sort of tribute in that regard.

JuliusMarx says

I hear mathematicians always go in factors of n. (Whereas n is >2 and <4.)

Dan Burt says

Not to be so presumptuous, but here's my modest rewrite:

Mandelbrot's in heaven, unless he's somewhere else instead /
Right now his ghost is sighted teaching math at Yale

AllBWell says

I think it's a great song for a great man. I agree with not changing it.
Also, I just wanted to say thanks for all your great songs.

jblopez2020 says

your Mandelbrot song/homage is brilliant and quite appropriate; you inspire and challenge me as an artist, I'm very glad to have "accidentally" discovered you yesterday via the nerdist podcast archive.

Mixtapes says

For some reason this link never works. Great song however. I hope it's in the set list for sure.

Tindi says

I'm sad to hear he died; he was an interesting guy. As for the song, I like it either way.

To the point about understanding nature, I've always felt that, in and of itself, the drive to understand things is an interesting thing, but when you take it too far, you do lose that appreciation of the beauty of it all in the rush to find out more. I also agree that we can never FULLY understand it all; our brains are too crammed with all the other crap we have up there already. Besides, as other commenters have said, once you find "everything," what's next?

Falgaia says

Holy Cow, I just realized that Benoit Mandelbrot died on my birthday. Holy Cow. Some Birthday Present...

And I liked that song, too...

Now I feel guilty every time I hear it. +(

David Cloutman says

Mandelbrot's life was a miracle. By surviving the holocaust to bringing forth new and beautiful ideas, he defied totalitarian and the nationalistic ideologies of the early 20th century. Very few mathematicians, or pure intellectuals for that matter, inspire song, and regardless of the rectitude of his ideas, I sincerely hope that he is not forgotten.

Demetrius says

Maybe the respectful thing to do is to just replace the (newly) inaccurate verses with a moment of silence after "Mandelbrot's in heaven". We can sing along with the missing verses in our minds and hearts where he lives on!

Someone told me that Benoit Mandelbrot took the middle initial "B"... presumably, to stand for "Benoit B Mandelbrot". The fractal implications are awesome!